Combine the water and sugar in a small saucepan and cook over medium-high heat, stirring, until the mixture comes to a boil and the sugar has dissolved.,Let cool to room temperature.,Put the syrup, coconut milk, rum, and 3 cups of the pineapple in a blender and blend until smooth.,Let chill completely.,For each serving, put about 2 tablespoons of the remaining pineapple in a serving dish or glass.,______,If you have pineapple left over, place it on top.,Drizzle 6 to 8 tablespoons of the syrup over the top and garnish with the coconut.,Serve immediately.